\chapter[Vectors and Matrices \\ \textnormal{\emph{Lectured in Michaelmas \oldstylenums{2020} by \textsc{Dr.\ J.\ M.\ Evans}}}]{Vectors and Matrices}
\emph{\Large Lectured in Michaelmas \oldstylenums{2020} by \textsc{Dr.\ J.\ M.\ Evans}}

The complex numbers can be viewed as a kind of two-dimensional analogue to the real numbers, with a real coordinate and an imaginary coordinate.
Euclidean space is a three-dimensional version of the reals, with three coordinates to represent each point.
In this course, we generalise these examples, and study vector spaces which can have any dimension.

Functions between vector spaces that preserve the vector space structure are called linear.
Linear maps have many different useful properties.
One such property is the determinant: if the determinant is any number except zero, the linear map has an inverse function.

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